Problems wih Probability

[Dwayne]

Please help me understand how to solve the following problem:

If two fair dice are rolled, find the probability of a sum of 8, given that the sum is greater than 7.



Thank you for your assistance!

 

[Gene]

Picture an array with 1-6 across he top and 1-6 down the sde with the sums filled in the intersections. We eliminate the upper left triangle 'cause they are all less than or = 7 which leaves a 5 by 5 triangle of the lower right for 15 possibilities. Five of them are 8 so 5/15 = 1/3

 

[stapel]

How many possible sums are there? (This is where you do that six-by-six grid, filling in the squares with the sums of the two dice.)

How many of these sums are greater than 7?

Of these, how many are equal to 8?

Eliz.

 

[soroban]

Hello, Dwayne!

I will assume you've done "dice" problems before
. . and that you know about the 36 possible outcomes.

If two fair dice are rolled, find the probability of a sum of 8, given that the sum is greater than 7.

We are <u>given</u> that sum is greater than 7.

So there are 15 possible rolls:
. . 2-6, 3-5, 4-4, 5-3, 6-2, 3-6, 4-5, 5-4, 6-3, 4-6, 5-5, 6-4, 5-6, 6-5, 6-6

Of the fifteen rolls, five have a sum of 8.

Therefore: .\(\displaystyle P(\text{sum of }8\,|\,\text{sum of }7) \;= \;\frac{5}{15}\;=\;\frac{1}{3}\)

 

[Dwayne]

I think I was reading too much into it. Thanks everyone for the clarification!